Digital techniques in signal processing provide several advantages over analog signal processing. Digital systems are typically implemented with programmable digital signal processors (DSPs), which permits a designer to change system functions by reprogramming the DSP. For instance, a DSP implemented filter may be altered by merely changing the DSP programming. Digital systems are also more stable with respect to environmental conditions than systems implemented with discrete analog components, such as resistors and capacitors. Unlike a filter implemented with discrete analog components, a digitally implemented filter will not change its characteristics within the operating temperatures of the digital components. A DSP based system also permits the designer to easily implement error correcting schemes or functional algorithms that are not easily implemented by the analog designer. For these reasons, digital signal processing techniques are now widely used in communications, audio and video systems, control systems and robotics.
With the advent of the compact disc (CD) player, digital techniques are used in almost all audio systems where high psychoacoustic sound quality is desired. To faithfully reproduce audio in a digitally based system, the bandwidth of the sampled signal may not exceed one-half of the sampling frequency. The minimum sampling frequency for reproducing a given signal is known as the Nyquist frequency. For instance, in an audio system, the theoretically minimum sampling frequency is twice the audio bandwidth, or 40 kHz. In actuality, a CD player uses a frequency of 44.1 kHz, theoretically permitting reproduction of an audio signal having a signal component at 22.05 kHz.
One limiting factor in a digital audio system is the dynamic range of the system's digital to analog converter (DAC). The theoretical dynamic range is limited by the DAC's resolution, and is given by the formula: dynamic range (dB)=6.02n+1.76, where n equals the number of bits of resolution. Also known as signal to error ratio, application of the formula is explained in Pohlmann, Principles of Digital Audio, 2d edition, Howard W. Sams & Co. at page 61., and in Gaddy and Kawai, Dynamic Performance Testing of Digital Audio D/A Converters, Application Bulletin, Burr-Brown Corporation, 1997, at page 3. According to Gaddy and Kawai, dynamic range is perhaps the most useful figure of merit for a DAC in an audio application, because it indicates the DAC's ability to reproduce low level signals. Human hearing is more sensitive to distortion at low level signals than at high level signals.
To attain high sound quality, a typical pulse-code modulated digital audio system maintains a 24 bit internal resolution for presentation to a 16 bit DAC. While there are DACs that accept a 24 bit input, no 24 bit digital system performs at a true 24 bit level. According to theoretical signal to error calculations, such a system should achieve a dynamic range of 146 dB. In practical applications, however, a much lower dynamic range is achieved, and, in a 24 bit system, a dynamic range of 134 dB (22 bit level) is rarely, if ever, surpassed. This reduced dynamic range is due at least in part to random errors in the DAC, which may in turn be caused by non-linearities in the DAC and by semiconductor noise.
Various schemes are now used for improving DAC performance in audio systems. For instance, a DAC for a digital audio system may have its output noise-shaped, which compensates for the non-flat response curve of typical human hearing. Much of the industry effort has been in the design and fabrication of integrated circuit or hybrid DACs that exhibit incrementally higher levels of performance. Nevertheless, even the best 24 bit DACs available for digital audio applications do not surpass the 22 bit level of performance. A demand remains, therefore, for better dynamic range and for playback sound higher in psychoacoustic sound quality than is currently achieved in digital audio systems.